Sergei G Matinyan and Berndt Müller 2006 J. Phys. A: Math. Gen. 39 L285 doi:10.1088/0305-4470/39/18/L05
Sergei G Matinyan1,3 and Berndt Müller2
Show affiliationsWe study the semiclassical Wigner–Kirkwood (WK) expansion of the partition function Z(t) for arbitrary even homogeneous potentials, starting from the Bloch equation. As is well known, the phase-space kernel of Z satisfies the so-called Uhlenbeck–Beth equation, which depends on the gradients of the potential. We perform a chain of transformations to obtain novel forms of this equation that invite analogies with various physical phenomena and formalisms, such as diffusion processes, the Fokker–Planck equation and supersymmetric quantum mechanics.
03.65.Sq Semiclassical theories and applications
02.30.-f Function theory, analysis
81S30 Phase space methods including Wigner distributions, etc.
82B10 Quantum equilibrium statistical mechanics (general)
81Q20 Semiclassical techniques including WKB and Maslov methods
Issue 18 (5 May 2006)
Received 22 January 2006, in final form 28 March 2006
Published 19 April 2006
Sergei G Matinyan and Berndt Müller 2006 J. Phys. A: Math. Gen. 39 L285
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